# Algebra and Trigonometry Enhanced with Graphing Utilities by Michael Sullivan, Michael Sullivan III

By Michael Sullivan, Michael Sullivan III

Michael Sullivan’s time-tested strategy focuses scholars at the basic abilities they wish for the path: preparing for category, practicing with homework, and reviewing the ideas. The Enhanced with Graphing Utilities Serieshas advanced to fulfill today’s direction wishes via integrating the use of graphing calculator, active-learning, and expertise in new how one can support scholars prevail of their path, in addition to of their destiny endeavors.

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20 CHAPTER R Review EX AM PL E 3 Computing Absolute Value (a) 0 8 0 = 8 (b) 0 0 0 = 0 (c) 0 -15 0 = -( -15) = 15 Look again at Figure 15. The distance from -4 to 3 is 7 units. This distance is the difference 3 - ( -4), obtained by subtracting the smaller coordinate from the larger. However, since 0 3 - ( -4) 0 = 0 7 0 = 7 and 0 -4 - 3 0 = 0 -7 0 = 7, we can use absolute value to calculate the distance between two points without being concerned about which is smaller. DEFINITION If P and Q are two points on a real number line with coordinates a and b, respectively, the distance between P and Q, denoted by d(P, Q), is d(P, Q) = 0 b - a 0 Since 0 b - a 0 = 0 a - b 0 , it follows that d(P, Q) = d(Q, P).

B) On the real number line, graph all numbers x for which x … 5. Solution Figure 13 Ϫ2 Ϫ1 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 (a) See Figure 13. Notice that we use a left parenthesis to indicate that the number 4 is not part of the graph. (b) See Figure 14. Notice that we use a right bracket to indicate that the number 5 is part of the graph. Figure 14 Now Work Ϫ2 Ϫ1 0 PROBLEM 31 2 Find Distance on the Real Number Line Figure 15 4 units Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 3 units 0 1 2 3 4 DEFINITION The absolute value of a number a is the distance from 0 to a on the number line.

05388 521 15 38. 81 5 In Problems 39–48, write each statement using symbols. 39. The sum of 3 and 2 equals 5. 40. The product of 5 and 2 equals 10. 41. The sum of x and 2 is the product of 3 and 4. 42. The sum of 3 and y is the sum of 2 and 2. 43. The product of 3 and y is the sum of 1 and 2. 44. The product of 2 and x is the product of 4 and 6. 45. The difference x less 2 equals 6. 46. The difference 2 less y equals 6. 47. The quotient x divided by 2 is 6. 48. The quotient 2 divided by x is 6.